Complete characterization of stationary logit equilibria

Characterize the existence, uniqueness, and local asymptotic stability of stationary logit equilibria for the SIS epidemic model with logit behavioral learning across the remaining parameter spaces not covered by the sufficient conditions established in the paper.

Background

The paper derives sufficient conditions guaranteeing the existence, uniqueness, and local asymptotic stability of disease-free, interior endemic, finite-rationality endemic, and corner endemic stationary logit equilibria in selected regions of the epidemic and payoff parameter space. These conditions do not cover all possible combinations of transmission, recovery, and payoff-difference parameters.

The authors explicitly identify the unresolved task of determining the equilibrium structure in the remaining parameter regions, making this a direct open problem concerning the full coupled SIS–logit dynamical system.

References

While we have derived several conditions that guarantee the existence, uniqueness and LAS of the SLE, this paper does not present a complete characterization of the equilibria, and exploring the remaining parameter spaces remain an open challenge for future research.

— SIS Epidemic Containment under Game-theoretic Rational Learning  (2610.03173 - Maitra et al., 2 Oct 2026) in Section 4, subsection “Existence of SLE”; Section 7, “Conclusions and Future Work”